Compressibility of $\mathrm{Ce}M{\mathrm{In}}_5$ and ${\mathrm{Ce}}_{2}M{\mathrm{In}}_8$ ($M=\mathrm{Rh}$, Ir, and Co) compounds

The lattice parameters of the tetragonal compounds $\mathrm{Ce}M{\mathrm{In}}_5$ and ${\mathrm{Ce}}_{2}M{\mathrm{In}}_8$ ($M=\mathrm{Rh}$, Ir, and Co) have been studied as a function of pressure up to $15\mathrm{GPa}$ using a diamond anvil cell under both hydrostatic and quasihydrostatic conditions at room temperature. The addition of $M{\mathrm{In}}_2$ layers to the parent $\mathrm{Ce}{\mathrm{In}}_3$ compound is found to stiffen the lattice as the 2-layer systems (average of bulk modulus values $B_0$ is $70.4\mathrm{GPa}$) have a larger $B_0$ than $\mathrm{Ce}{\mathrm{In}}_3$ $\left(67\mathrm{GPa}\right)$, while the 1-layer systems are even stiffer (average of $B_0$ is $81.4\mathrm{GPa}$). Estimating the hybridization using parameters from tight binding calculations shows that the dominant hybridization is $fp$ in nature between the Ce and In atoms. The values of $V_{pf}$ at the pressure where the superconducting transition temperature $T_c$ reaches a maximum is the same for all $\mathrm{Ce}M{\mathrm{In}}_5$ compounds. By plotting the maximum values of the superconducting transition temperature $T_c$ versus $c∕a$ for the studied compounds and Pu-based superconductors, we find a universal $T_c$ versus $c∕a$ behavior when these quantities are normalized appropriately. These results are consistent with magnetically mediated superconductivity.

Figure 1

X-ray diffraction patterns of $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_5$ at ambient pressure and a hydrostatic pressure of $4.2\mathrm{GPa}$. The data were taken using synchrotron radiation of wavelength $\lambda =0.37214\mathrm{\AA }$. The various reflections from $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_5$ are labeled and one peak due to excess In flux is noted.

Figure 2

Normalized volume $V∕V_0$ and ratio of tetragonal lattice constants $c∕a$ plotted versus pressure for $\mathrm{Ce}M{\mathrm{In}}_5$ compounds at room temperature. Data for both quasihydrostatic (open symbols) and hydrostatic (closed symbols) are displayed. The solid line through the volume data is a fit as described in the text. The dashed vertical lines in the $c∕a$ plots show the pressure where the maximum value of $T_c$ is observed. The solid lines in the $c∕a$ plots are guides for the eye.

Figure 3

Normalized volume $V∕V_0$ and ratio of tetragonal lattice constants $c∕a$ plotted versus pressure for ${\mathrm{Ce}}_{2}M{\mathrm{In}}_8$ compounds at room temperature. Data for both quasihydrostatic (open symbols) and hydrostatic (closed symbols) are displayed. The solid line through the volume data is a fit as described in the text. The dashed vertical lines in the $c∕a$ plots show the pressure where the maximum value of $T_c$ is observed. The solid lines in the $c∕a$ plots are guides for the eye.

Figure 4

The ambient pressure values of the superconducting transition temperature versus the room temperature value of $c∕a$ (open circles) for various $\mathrm{Ce}M{\mathrm{In}}_5$ compounds. Also shown (solid circles) are the values of $c∕a$ determined at room temperature at the pressure $P_{\max }$ where $T_c\left(P\right)$ displays a maximum. The line is a least squares fit to the ambient pressure values.

Figure 5

Schematic phase diagram for the $\mathrm{Ce}M{\mathrm{In}}_5$ compounds showing the competition between magnetic order and superconductivity. For small values of the hybridization $V^2$, the magnetically ordered state (dashed line) is favored. As pressure is applied, systems move to the right in the diagram and the magnetically ordered state gives away to superconductivity (solid lines). The approximate ambient pressure position is shown for various $\mathrm{Ce}M{\mathrm{In}}_5$ materials. The superconducting curve for $\mathrm{Ce}\mathrm{Rh}{\mathrm{In}}_5$ lies between the $\mathrm{Ce}\mathrm{Ir}{\mathrm{In}}_5$ and $\mathrm{Ce}\mathrm{Co}{\mathrm{In}}_5$ curves.

Figure 6

The ambient pressure values of $T_c∕T*$ versus the room temperature value of $\Delta (c∕a)$ (open symbols) for various ${\mathrm{Ho}}_n\mathrm{Co}{\mathrm{Ga}}_{2n+3}$ based compounds; $\mathrm{Ce}M{\mathrm{In}}_5$ (circles), ${\mathrm{Ce}}_{2}M{\mathrm{In}}_8$ (diamonds), and $\mathrm{Pu}M{\mathrm{Ga}}_5$ (squares) are all shown. Also shown (solid symbols) are the values of $\Delta (c∕a)$ determined at room temperature at the pressure $P_{\max }$ where $T_c\left(P\right)$ displays a maximum. The straight line is the same as that shown in Fig. 4.